COULOMB INTERACTION OF He -like IMPURITY IN SEMIMAGNETIC QUANTUM DOT P.Kalpana, P.Nithiananthi and K.Jayakumar* Nanostructure lab, Department of Physics, Gandhigram Rural University, Gandhigram, Tamilnadu, India *kjkumar_gri@rediffmail.com

Spintronics A new class of device based on the Quantum of electron spin, rather than on charge, may yield next generation of microelectronics

SPINTRONICS – Interplay of the Spin / Charge / Photon creates a better world than with the today’s microelectronic devices Spin Transport Photon (Magnetism) Charge (Electronics) Magneto Optical IC Spin -LED Quantum Computer MRAM Spin - FET

Why Spin? Connection between spin and magnetism Intrinsic connection between spin and quantum mechanics Short range spin – dependent exchange interactions Speed and Power Dissipation Long coherence or relaxation

Giant Magneto Resistance To some people, 10 years = a decade. To IBM Research, 10 years = a revolution. a very large change in electrical resistance in a ferro magnet / para magnet multi layer structure. – Makes it’s mass market debut in IBM’s record breaking 16.8 gigabyte hard disk for desktop computers

Spins and Scattering An electron moving into a magnetized region will exhibit spin-dependent scattering Electrons with spins in the direction of the magnetic field will scatter less than electrons with spins opposite the direction of the magnetic field Magnetization

GMR in Magnetic Layered structures – without magnetic field Alternate layers of ferromagnetic material will naturally align with opposite magnetization All electrons coming in will scatter since they’ll have opposite spin from magnetization in some region Ferromagnetic material with magnetization in direction of turquoise arrow Non-ferromagnetic material spacer

GMR in Magnetic Layered structures – with magnetic field If an external field is present, ferromagnetic layers will all align with external field Only half of the electrons coming in will scatter maximally, those with spin opposite external field Ferromagnetic material with magnetization in direction of turquoise arrow Non-ferromagnetic material spacer Externally applied magnetic field

Datta – Das Spin Transistor – First spintronic device

Why Diluted magnetic semiconductors (DMS)? Crucial element for the success of spintronics – To find a proper material that combines the desirable properties of ferromagnetism and semiconductors Role of the interface separating different materials and how to create and measure spin polarization Spin Injection Spin Transport Spin Detection Normal metal –Semiconductor contacts Directly injecting spins from Ferro magnet into a nonmagnetic semiconductor Obtained spin polarization substantially smaller Do not amplify signals Complete picture of transport across the interface is not yet available

Reduces the significant material differences Advantages: Reduces the significant material differences Provides Spin Polarized Carriers Diluted Magnetic Semiconductors –Magnetic ions partially substitutes the Cations in the host lattice and become diluted semiconductors , where x – Magnetic ion concentration Eg: CdTe/Cd1-xMnxTe, GaAs/Ga1-xMnxAs Concentrated Diluted Non - magnetic Magnetic Semiconductor Magnetic Semiconductor Semiconductor Magnetic ion Cation Anion

INTRODUCTION: DILUTED MAGNETIC SEMICONDUCTORS Magnetic Semiconductors basically a Semiconductor with filled Valance Band and empty Conduction Band. Energy bands can be described by band theory similar to ordinary Semiconductors. Wavefunctions are Bloch functions – not localized at a particular atom but extending over the entire crystal.

Mn as an impurity: II-VI vs III-V II III IV V VI Si P Sn Se Zn Hg Cd B C Al N O S Ga Ge In As Sb Te Mn (III, Mn)-V (Ga,Mn)-As (In,Mn)-As (II,Mn)-VI (Cd,Mn)-Te Mn in III-V semiconductors: acceptor level below VB top (hole picture!) → hydrogenic acceptor level Mn3+ becomes Mn2+ (spin 5/2) + weakly bound hole Mn in II-VI semiconductors: no levels in gap, stable Mn2+ (half filled) → only introduces spin 5/2, no carriers

IMPORTANCE OF (II,VI)Mn DMS Smaller Defect Concentrations and easier to dope with shallow impurities Tunability of their lattice parameters and their energy gaps Preparation of quantum wells, superlattices, bandgap engineering Why CdTe, Particular? Direct band gap Crystal structure – Zinc Blende Bandwidth intermediate between narrow and high

Electronic configuration for Cd – 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 Te - 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p4 Mn - 1s2 2s2 2p6 3s2 3p6 3d5 Exciting combination of both magnetic and Semimagnetic properties. Exhibit magnetic hysteresis effect Magnetic Compounds – in general contain transition metal atom with partially filled d – shells Electronic states are derived from 3d – orbitals e- s in these d – state are more localized which are responsible for localized magnetic moment in Magnetic Semiconductor.

Exchange Interaction between Charge Carrier and localized Ferro magnet has spontaneous magnetic moment i.e e- spin and magnetic moment arranged in regular manner and there is an internal interaction tending to line up the magnetic moment parallel to each other – exchange field This exchange interaction orient magnetic moment leading to net magnetization below Tc. Exchange Interaction between Charge Carrier and localized magnetic moment g = Lande Splitting Factor B = Bohr Magneton  = g B Sn Magnetic atom Sn S Rn Conduction e- r

The Hamiltonian for conduction electron interacting with magnetic atom is given by Unperturbed Interaction between Interaction between Hamiltonian conduction e- & localized moments magnetic moment

Giant Zeeman Splitting  

BOUND MAGNETIC POLARONS IN SEMICONDUCTOR LATTICE Because of polarization of the spin system there is a possibility of charge carrier might be self trapped – Magnetic Polaron These electrons lie in their hydrogenic orbital with characteristic Bohr radii As their concentration increases , their individual orbits extends out into narrow impurity bands The electron interacts with all the magnetic ions that lied within that orbit. Each electron has an exchange interaction with all the magnetic ions lying within it’s orbital or ‘Sphere of influence’ If there are large enough number of magnetic spins within the orbital , the electron is completely spin polarized The atomic magnetic moments have an indirect exchange interaction mediated by the carriers, that results in ferromagnetic ordering BOUND MAGNETIC POLARONS IN SEMICONDUCTOR LATTICE

IMPURITY DOPING OF CdTe AND CdMnTe Un intentional Or Intentional Donors Acceptors Shallow Deep Indium Dopants, Halogen Atoms n-type CdTe P, As and Sb Dopants p-type CdTe Impurities Doping Not only Provides free carriers but undesired formation of deep defects

He – like IMPURITY In CdTe/Cd1-xMnxTe Quantum Dot Z Energy Conduction band Cd1-xMnxTe CdTe EB Esub <H>min

Quantum Mechanical Tunneling Classical electrodynamics - forbids flow of current through an insulating barrier M Sc / I M e- Application – has voltage – non vanishing probabaility for an e- to tunnel through I – barrier giving rise to flow of current Quantum Mechanics

Single electron Transistor The single-electron tunneling transistor - a device that exploits the quantum effect of tunneling to control and measure the movement of single electrons was devised. Experiments have shown that charge does not flow continuously in these devices but in a quantized way.

Coulomb Blockade a) When a capacitor is charged through a resistor, the charge on the capacitor is proportional to the applied voltage and shows no sign of quantization. (b) When a tunnel junction replaces the resistor, a conducting island is formed between the junction and the capacitor plate. In this case the average charge on the island increases in steps as the voltage is increased (c). The steps are sharper for more resistive barriers and at lower temperatures.

Coulomb Interaction and the Binding of He like impurity in Semimagnetic Cubical Quantum Dot (CQD) Under Square Confinement

THEORETICAL FRAMEWORK Methods used EFFECTIVE MASS APPROXIMATION VARIATIONAL PROCEDURE GROUND STATE IMPURITY ENERGY

barrier model) in the effective mass approximation is given by The Hamiltonian of the two donor electrons in a CdTe/Cd1-xMnxTe QD (in the finite barrier model) in the effective mass approximation is given by where, g = ħwc/2R* (wc – cyclotron frequency) is the parameter of the strength of the magnetic field and (g =1 corresponding to 30.5604 Tesla). The effective confinement potential for the cubical QD is given as, where, L = size of the CQD and V0=70%DEgB.

The external applied magnetic field strongly changes the difference in the band gap between Cd1-xMnxTe and CdTe by[1] - Band gap difference between Cd1-xMnxTe/CdTe without magnetic field. - is chosen with  as a parameter(=0.5) and 0 as the critical magnetic field which depends upon the value of the composition ‘x’ Eg (Cd1-xMnxTe) = 1606 + 1587x (meV). The critical field (in Tesla) for other values of composition (x) is given as B0 = A2exp[nx], where, A2 = 0.734 and n=19.082. The trial wavefunction for the singlet ground state is chosen as

evaluate the electron – electron interaction energy. Where, a=(2m*E/3)1/2, b=(2m*(V0-E)/3)1/2 and  is the variational parameter and Cee is obtained from the continuity condition The minimum of the Hamiltonian is evaluated and the variational parameter λ is fixed in the wave function ψ1s (r1, r2) and this wavefunction is used to evaluate the electron – electron interaction energy. The lowest energy (E) without the donor impurity is obtained by using the transcendental equation The binding energy of double donors in the presence of magnetic field is found by solving the Schrödinger equation variationally, and is given by

Electron-Electron interaction energy against Dot size for x=0 Electron-Electron interaction energy against Dot size for x=0.3 for various magnetic fields. On CentreIE > On EdgeIE For Narrow Dot size, There is no appreciable difference between OC and OE Interaction energy because of the behaviour of the wavefunction. For L < 90Å, IE as the magnetic field Turnover occurs at higher magnetic field B

(W a 1/L2), W = Effective confinement frequency (VCoulomb a 1/L), Vcoulomb = Interaction energy between donor electrons, L = Dot Size Decreasing Dot Size Increasing Dot Size

Attributing the turnover feature to the interplay between three forces At lower QD radius the repulsive force gain in strength and causes tunneling which in turn reduces the IE Attractive Force due to the confining potential in a dot that tends to confine the electrons together Repulsive force due to the Coulomb interaction between the electrons themselves Magnetic field which reduces the confinement and aids the repulsive forces. First B Second Third

electron-electron interaction energy against Dot size for x=0 electron-electron interaction energy against Dot size for x=0.3 for various magnetic fields. A shallow to deep transition of the Binding Energy (BE) as the dot size reduced, since the < Potential > seen by the electrons becomes more negative (Attractive) as Dot size (L) reduces When g = 5 critical field, BE decreases because of the reduced barrier height BE for OC impurity than OE impurity because of the delocalization of the e- wavefunction towards the Cd1-xMnxTe barrier since the barrier potential increases (Interaction of Mn2+ in the barrier and the external magnetic field) . But for g = 5, No appreciable difference in BE When impurity is at zi=0 and zi= L/2, because the amount of increase of KE and PE for OC and OE impurity is of the same order

Drastic difference in Potential Energy of Mn2+ on the carriers and low expectation value of PE even though the KE increases, upto 100Å Beyond 100Å, the OE binding energy for g=0 << both OC and OE binding energy for g=5 only because of the predominance of potential energy Variation of potential energy of Mn2+ on the carriers (meV) against dot size for with and without magnetic field Dot Size (Å) g=0 zi=L/2 g=5 50 5.39942 11.3271 70 0.550539 8.34648 90 0.0927 5.92756 100 0.0432685 3.86741 200 0.0002235 0.00389589 250 0.0000004 0.00046741 350 0.0000001 0.0000005

Conclusions Both BE and IE is larger only when the impurity is at on center of the well This behaviour is slightly changed in the narrower dot region when the magnetic field is applied externally. This work will be very useful for understanding the Coulomb blockade in Nanostructured systems and to understand the two particle spectra also.

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